Hindawi Journal of Advanced Transportation Volume 2021, Article ID 5595065, 18 pages https://doi.org/10.1155/2021/5595065
Research Article A Monitoring Approach Based on Fuzzy Stochastic P-Timed Petri Nets of a Railway Transport Network
Anis M’hala
Laboratory of Automation, Electrical Systems Environment (LAESE), National Engineering School of Monastir (ENIM), Monastir, Tunisia
Correspondence should be addressed to Anis M’hala; [email protected]
Received 8 January 2021; Revised 1 April 2021; Accepted 5 April 2021; Published 27 April 2021
Academic Editor: Socrates Basbas
Copyright © 2021 Anis M’hala. *is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. *is paper proposes a monitoring approach based on stochastic fuzzy Petri nets (SFPNs) for railway transport networks. In railway transport, the time factor is a critical parameter as it includes constraints to avoid overlaps, delays, and collisions between trains. *e temporal uncertainties and constraints that may arise on the railway network may degrade the planned schedules and consequently affect the availability of the transportation system. *is leads to many problems in the decision and optimization of the railway transport systems. In this context, we propose a new fuzzy stochastic Petri nets for monitoring (SFPNM). *e main goal of the proposed supervision approach is to allow an early detection of traffic disturbance to avoid catastrophic scenarios and preserve stability and security of the studied railway networks. Finally, to demonstrate the effectiveness and accuracy of the approach, an application to the case study of the Tunisian railway network is outlined.
1. Introduction derailment, which happened near Sahline, 10 km south of Sousse, is especially relevant (numerous injured passengers). Railway industry plays a critical role in transportation and transit *e inquiry commission determined that the accident resulted systems attributed to the ever-growing demand for catering to from failure of the railroad switch, holding the maintenance both freight and passengers. However, owing to many challenges company responsible for the failure. In this context, it is es- faced by railway stations such as harsh environments, traffic sential to develop a supervision approach allowing to avoid flow, safety, and security risks, new and adaptive systems catastrophic scenarios and to further rail safety. employing new technology are recommended [1]. Our study is devoted to the modeling and monitoring of In the railway transport system, the processing times are the Tunisia railway transport networks by using stochastic interval-valued with parameters that depend on the oper- P-timed Petri nets in order to control traffic and to avoid ation to be performed. Any deviations from the specified disruptions problems. *e approach proposed in this paper interval will characterize a traffic disturbance. Consequently, is based on a statistical analysis of the real measurements, the monitoring of the time intervals will be used as the main collected by the Supervisory Control and Data Acquisition principle to detect and isolate the disturbances that affect the (SCADA) system of the Tunisian National Railway Company system. *e system that motivated this study is a real railway (TNRC), to identify the time parameters of the stochastic transport network in Tunisia. P-timed Petri net (SP-TPN) model. In particular, the ap- To reduce road congestion in urban areas, railway proach determines the dynamic time intervals associated networks are coming under increasing strain. In Tunisia, with the places of the SP-TPN and the resulting probability integrity rail services are operated in many metropolitan density functions (PDF) of the travelling and parking times. areas but most notably in the Tunisian Sahel region. *e main objectives are to analyze the traffic conditions by Safety is of critical concern, particularly given the recent simulation and to monitor the traffic by avoiding possible high-profile rail accidents featured in the media. *e metro troubles and perturbations. 2 Journal of Advanced Transportation
Our study concerns the Tunisian railway transport including advanced WSNs, which will enhance security, system, particularly, in the Tunisian Sahel region. *is safety, and decision-making processes to achieve more cost- system must respond to different requirements, minimizing effective management in railway stations, as well as the the waiting times in the stations, respecting schedules, and development of integrated systems. *e authors demon- ensuring the safety of passengers and equipment. In our strate that the size, efficiency, and cost of WSNs are influ- previous works [2], synchronized Petri nets (P-TPNs) are ential factors that attract the railway industry to adopt these used to model railway transport systems. In this way, the devices. modeling process is greatly simplified, and the complexity of Kulbovskyi et al. [11] propose a new monitoring ap- the model is widely reduced. In [2], an identification of the proach for a power supply network system. *e proposed P-TPN model of the Sahel railway network in Tunisia was monitoring model shows information chains between sys- made. *e objective was to identify the temporal parameters tem components and their object, generalized structure of of the model from a set of real measurements collected by the original data flow-over, particulrly, controlling decisions SCADA system of TNRC. and external effects within the information and computer *e contributions of the present paper are as follows: system. In order to identify emergency and abnormal op- erating regimes of electrical networks in real-time mode, an (i) *e improvement of the time semantic of the railway application to railway power supply network was proposed. network model with the introduction of the sto- *e development of algorithms for detecting failures in chastic P-timed Petri nets (SP-TPNs) railway catenary support components was proposed by Liu (ii) A new supervision approach, based on the study of et al. [12]. In this context, virtual reality technology is effective sojourn time of the token in places and the employed to control the learning environment of con- evaluation of the probability density functions (PDF) volutional neural networks (CNNs) for the automatic of the travelling times, is proposed. *is approach is multicamera-based monitoring of catenary support com- used to evaluate the influence of different types of ponents. First, 3D image data based on drawings and real- disturbances on the expected schedule. life video images are developed. *en, a virtual reality en- *is paper is organized as follows. Section 2 presents the vironment for monitoring the railway catenary support state of the art. Section 3 presents the studied railway system is created, emulating real-life conditions such as transport system and the SP-TPN model of the railway measurement noise and a multicamera train simulation to network of the Sahel Tunisia. Afterward, the problem of resemble state-of-the-art monitoring systems. monitoring of railway transport networks is tackled. An On the other hand, Mishra [13] proposed an anticolli- original supervision approach based recovery approach sion system named “TMCAS” (train monitoring and col- based on stochastic P-timed Petri nets is presented. lision avoidance system) that uses a protocol to share and In Section 5, an application of the developed monitoring exchange position, speed, and the signal at danger infor- approach to realistic railway is proposed. Finally, a con- mation between trains and central control room. TMCAS clusion is presented with some perspectives. aims to automate train operations and act as a safety en- hancement system by ensuring speed control, rear-end and 2. State of the Art head-on collision avoidance, and signal-at-danger avoidance. Railway transport systems must be monitored online to Some other works are interested in the online moni- avoid situations that may be critical because of disturbances. toring of railway traffic in presence of unpredictable events. *ese disturbances can affect the railway infrastructure or Pinto et al. [14] presents a contactless system to measure traffic management, and that they can lead to a degradation track displacements and its application in an embankment/ of the transport service. *e general objective is to maintain underpass transition zone, located on the Northern line of the stability of the railway network and make it more effi- the Portuguese railway network where the Alfa Pendular cient and secure. In this context, various research projects tilting train travels at a maximum speed of 220 km/h. *e were conducted on the monitoring of transportation systems system is based on a diode laser module and a position to save time and improve the quality of rail service [3–9]. sensitive detector (PSD). *e PSD receives the laser beam Among many related research studies, Bennet et al. [10] emission, and the detection of the center of gravity of the propose an identification of the critical factors that should be beam spotlight on the PSD area enables the calculation of the considered in the design of a wireless sensor network, in- displacement. *e optical measuring system proved to be an cluding the availability of electrical power and communi- efficient and flexible way to measure absolute and relative cations networks in railway transport. Various issues facing rail displacements in the field, enabling the detection of track underground deployment of wireless sensor are discussed, in deformability differences along the transition zone. particular, for two-field case studies involving networks *e work presented by Ciampoli et al. [15] reports on the deployed for structural monitoring in the Prague Metro and experimental activities carried out on a test-site area within a the London Underground. railway depot in Rome, Italy. In particular, combinations of In [1], the authors present a review of wireless sensor varying scenarios of fragmentation and fouling of the ballast networks (WSNs) that have been designed for use in were reproduced. *e setup was then investigated using monitoring and securing railway stations. Several WSNs different multifrequency of ground penetrating radar (GPR) applications are proposed for use in railway station systems, horn antenna systems. *ese were towed along the rail Journal of Advanced Transportation 3 sections by means of a dedicated railway cart. Interpretation Definition 1 (see [20]). A SP-TPN system is a triplet < R, IS, of the preliminary results has shown viability of the GPR IR>, where method in detecting signs of decay at the network scale, (i) R is a Petri net system thereby proving this technique to be worthy for imple- + + mentation in monitoring systems. (ii) IS: P ⟶ Q × (Q ∪ {+∞}) such that ISi � [ai, bi] To ensure the safety of railway operations and reduce the with 0 ≤ai ≤ bi is the static interval associated to the maintenance costs, a satellite synthetic aperture radar place pi (InSAR) system is presented by Wang et al. [16]. *e (iii) IR: P ⟶ Q+ × (Q+ ∪ {+∞}) such that IR � [α , β ] proposed InSAR provides a potential solution for a con- i i i with a ≤ α ≤ β ≤ b is the dynamical interval asso- secutive structural health monitoring of transition zones i i i i ciated to the place p with bi-/triweekly data update and mm-level precision. To i demonstrate the feasibility of the InSAR system for moni- ISi defines the static interval of staying time of a mark in + toring transition zones, a transition zone is tested. *e re- the place pi belonging to the set of places P (Q is the set of sults show that the differential settlement in the transition positive rational numbers). A mark in the place pi is taken zone and the settlement rate can be observed and detected by into account in transition validation when it has stayed in pi the InSAR measurements. at least a duration ai and no longer than bi. After the du- All previous works are different from our work. In our ration bi, the token will be dead. article, a new supervision approach allows to recognize In the railway network, each parking and travelling abnormal behaviors and traffic disturbances with the co- operation is associated with a time interval ([ai, bi] with u.t operation of the sojourn time and the probability density (unit time)). Its lower bound indicates the minimum time functions (PDF) associated with the travelling times. To the needed to travelling, and the upper bound sets the maximum best of our knowledge, such monitoring approach has been time not to exceed in order to avoid the traffic disturbances. never formalized for railway transport networks. Consequently, SP-TPNs have the capability of modeling time intervals and deducing a set of scenarios, when time 3. Tunisian Railway Network constraints are violated. 3.1. Presentation. *e railway line of the Sahel Tunisia en- sures the transportation of passengers and connects the main cities and agglomerations in the Sahel Tunisia from 3.2.1. A Stochastic P-Timed Petri Net Model of the Railway Sousse to Mahdia. *is metro line is 70 km long, and it is Network. *e objective of the SP-TPN modeling of the totally electrified. *e trains that run on the line make the transportation networks is to obtain a usable representation ride several times a day between 5 : 00 and 22 : 00, in an of the network to analyze the system and improve its average duration of 1h 30 minutes: 30 minutes between performance. Sousse and Monastir and 1 hour between Monastir and *e Sahel railway network is composed of three ter- Mahdia. It ensures the transport of more than 10 million minals stations (Mahdia, Monastir, and Sousse) and 28 passengers per year with an average traffic of 27 000 pas- stations: 20 stations between Mahdia and Monastir and 8 sengers per day. Figure 1 details the stations and durations stations between Monastir and Sousse. At the beginning of on the line train railway of the Sahel Tunisia between Mahdia the day, it is assumed that four trains start at Mahdia station, and Sousse stations. and 2 others are stationed at Sousse station. Figure 2 shows *e line begins from the Sousse Bab Jedid station until the SP-TPN model for the Sahel railway network. *e places Monastir station by serving the airport of Monastir, a part of P127,P128,P129,P130,P131, and P132 are source places initially the Monastir touristic zone and the University complex of marked to represent the parking of the trains. *e static Monastir. South of Monastir the line continues to Ksar intervals associated with these places are: IS127 � [2700, Hellal and Moknine cities and continues to Mahdia serving 2760], IS128 � [5100, 5160], IS129 � [7500, 7560], the cities of Teboulba, Bekalta, the tourist zone of Mahdia. IS130 � [9600, 9660], IS131 � [6000, 6060], and IS132 � [5700, 5760]. On this graph, the times associated to the places represent the durations of travels between two successive 3.2. Modeling of the Studied Railway Network by Stochastic stations. *e displacement of the tokens represents the P-Timed Petri Nets. Stochastic P-timed Petri nets (SP-TPNs) circulation of the trains on the railway. *e whole model has are a convenient tool to model the railway transportation 238 places and 126 transitions and more than 100 000 states networks with uncertainties and disturbances. SP-TPNs are a because 6 trains are assumed to be simultaneously in cir- subclass of timed Petri nets where stochastic durations are culation (this is the true situation in the considered railway associated with the places of the net [17–19]. In the considered network). application, the sojourn duration qi in each place pi represents A specific module for bidirectional segments is detailed either the stop at a station or the duration required to travel in [2] and used in Figures 2 and Figure 3. *e sojourn through a segment of the railway network. Such a duration duration qi in each place pi represents either the travelling has an expected value (qei) computed in order to satisfy the time between station or the parking times in stations. Such planned scheduled. Formally, SP-TPN models are inspired duration has an expected value (qie) which should be from Khansa et al. [20] and defined as follows: computed in order to satisfy the planned schedule. 4 Journal of Advanced Transportation
Sousse bab jedid
Monastir
Sousse Med.5 Sousse Sud Sousse Sousse Z.lnd Sahline Ville Sahline Sabkha Les Hôtels L'Aéroport Faculté La 4min
Mahdia 2min 3min 3min 3min 4min 3min 2min 6min
4min 3min 3min 3min 3min 3min 4min 2min 3min 2min2min2min2min 2min 2min 3min 3min 2min2min2min
14min Frina Lamta Savada Békalta Ezzahra Bouhjar Moknine Téboulba Baghdadi La Faculté La Ksar Hellal Ksar Borj El Arif Sidi Messoud Sidi Monastir Z.lnd Monastir Téboulba Z.lnd Téboulba Khniss–Bembla Moknine Gribaa Moknine Mahdia Z.Touris Mahdia K.Méd–Bennane Ksar Hellal Z.lnd Hellal Ksar Figure 1: Stations of the Sahel railway.
*e main parameters of the models are defined as who treated uncertainties, studied mainly two disturbances: follows: disturbances on the equipment (metro, train, traffic lights, security barrier etc.) or the disturbances concerning trav- (i) A train can park in a principal station at least one elling durations and, more particularly, the changes in minute. *e static intervals associated with the three staying and travelling times. For all these reasons, two main stations are ISp � ISp � ISp � [60, +∞] 1 45 63 functions of possibilities representing uncertainty over the (Figure 2). effective residence time (qi) of a token in a place pi and (ii) *e sojourn time of a metro in any other station is uncertainty on travelling time are proposed. *ese functions estimated from one to two minutes: ISi � [60, 120] make it possible to highlight traffic disturbances and help the (Figure 3). human agent in charge of detecting perturbations and de- (iii) At the beginning of each day, it is assumed that 4 ciding reconfiguration actions. trains start from Mahdia station, and 2 others are stationed at Sousse station (Figure 3). 4.1. Uncertainty on Travelling Time. *e proposed approach (iv) *e static intervals ISi and the effective sojourn time is based on the analysis of the measured behavior (departure qie associated with the stations and with the seg- ments between two successive stations are sum- times of the trains at the stations) and expected schedule. marized in Table 1. *e static intervals are defined From a sequence of experimental measurements observed based on the TNRC traffic dataset. during the operation of the Sahel rail transport system, the goal is to build a complete SP-TPN model capable of reproducing the observed behavior of the railway traffic. For 3.2.2. A Model of a Single Directional Segment. Figure 4 this purpose, the measured times will be used to determine shows a part of the SP-TPN modeling a single directional the dynamic intervals and the sojourn times for each place of segment. In the graph, the SP-TPN. (i) *e filled red places represent the stations (ii) *e empty white places represent the paths between 4.1.1. Collected Data from the TNRC Company. To identify two stations the parameters of the SP-TPN model, a set of real data is (iii) *e presence of a token at a place represents a train considered (see Table 2), that concerns the circulation of movement trains from Mahdia to Sousse and from Sousse to Mahdia on
Other places (places P185 and P186) (Figure 5) have been the Sahel railway network, during the month of June 2019. added to avoid the catching-up between two metros: if metro *e measurements have been recorded by the SCADA of the “M1” parks at a station P75, the latter cannot be caught by metro TNRC company. *e SCADA system allows to control “M2,” since the crossing of the transition T76 is conditioned by traffic, monitor, process real time, and record events. the presence of two tokens, respectively, at places P186 and P75. From an experimental point of view, at the end of each operation, the current real-time value is collected and stored 4. Uncertainty in Railway Network in TNRC database. *e identification of model parameters is based on a set of vectors showing the planned and measured *e railway traffic is subject to many uncertainties arising metro departure times at each station. All data and mea- from the travelling and staying time in stations. All authors, surements are reported in Table 2. Journal of Advanced Transportation 5
t81 IS = 60, ∞] p 45 p8 IS = [832, 848] 83 81 p45 IS83 = [111, 129] p172 t44 t82 t83 t84 p237 p23 Monastir 8 station t4 p44 IS82 = [60, 120] 3 IS = [60, 120] p205 117 IS IS = [60, 120] p 117 = [60, 120] 113 206 p82 p171 p117 p p IS 11 113 44 = [832, 848] p p208 236 t42 P43 p20 p22 IS43 = [60, 120]
t119 t118 t117 t116 t115 t114 t4 p42
p169
IS42 = [110, 130] IS41 = [60, 120] IS = [233, 247] p 118 118 p116 p114 p112 t107 t40 p4 …… p t120 t108 168 p170 IS116 = [170, 190] IS114 = [172, 188] p107 IS107 = [108, 132] IS112 = [175, 185]
P = {p / i = 84 ...p106} i i p p235 T = {t / i = 85 ...t } 108 p234 i i 106 t109 p Such as this sequence 231 includes 12 stations and 11 IS129 = [7500, 7560] IS108 = [60, 120] trips IS 109 = [230, 250] IS130 = [9600, 9660] p129 p23 p23 p130 p109 p230 p1 p 142 p143 p144 …… t 123 t124 IS 127 = [2700, 2760]
p1 P = {p / i = 22 ...p } IS12 = [60, 120] i i 40 t121 = { / = 21 ... } Ti ti i t39 IS = [60, ∞] Such as this sequence 1 p124 p123 p122 IS = [167, 193] includes Mahdi 111 IS = [171, 189] 110 9 stations and 10 a station p t110 p111 110 trips
t 11 t1 p137 p138 t112 t111 t122 t113 p p1 p p15 9 p15 14 IS = [60, 120] IS = [60, 120] 3 IS = [60, 120] 5 IS = [227, 253] 5 IS = [60, p14 16 9 p p p11 12 IS = [60, p 7 120] 15 p 5 120] 16 p3 t12 t 13 IS19 = [60, 120] p128 IS 17 = [60, 120] IS21 = [60, 120] 8 t9 t10 p19 p21 t2 t t p t15 p17 IS = [5100, 5160] t4 6 7 p10 13 128 IS = [168, IS 10 13 = [170, t5 t1 t3 192] 190] p119 p t17 t18 p120 121 t16 t20 p p8 p2 p4 t19
IS = [230, 250] IS = [172, IS = [174, IS = [173, 2 4 6 8 p p1 p20 188] 186] 187] 141 8 p139 p140 p145 IS = [168, 192] IS18 = [111, 129 20 Module VU for
p133 bidirectional segments p p p136 p146 1 135 p147
Figure 2: SP-TPN model for the Sahel railway network.
4.1.2. Computation of the Parking and Travelling Times. Each duration D(k) is decomposed into two times: the *e identification process aims to calculate the durations parking time at station and the travelling time between the between the stations. For this purpose, the duration between stations. One difficulty is that the SCADA does not collect the departure times in two successive stations is first separately these two times. *us, the parking times have computed: been estimated based on the expert knowledge of the TNRC operators: such times equal 50 seconds for main stations and D(k) � T(k) − T(k − 1). (1) 30 seconds for the other stations. Parking and travelling 6 Journal of Advanced Transportation
Staying duration Target from sousse to monastir
Sousse station
Monastir station
Travelling duration
Target from monastir to sousse
White places represent the paths between two stations Red places represent the stations Yellow resource places indicate the direction of train circulation Gray places represent two resources to avoid the collision and the crossover of the two trains Figure 3: SP-TPN model for the railway network Monastir_Sousse. times between Mahdia station and Sidi Massaoud station are 4.2. Effective Sojourn Time Uncertainty. To model the un- illustrated in Table 3 illustrates an example: certainties and disturbances that may affect the networks, the effective sojourn time qi in each place pi is computed according to a stochastic process of support IRi � [αi βi] such that a ≤α ≤ qe ≤ β ≤ b . *e effective sojourn duration q 4.1.3. Determination of the Duration Probability Density i i i i i i differs from the expected duration qei depending on the Functions. For each segment, the computation of the series disturbances Ω that occur in the network: of travelling and parking times during a period of several days leads to a collection of values that can be used to build a qi � qei + Ω. (2) stochastic model of the time behavior at the considered segment. In particular, we are interested in computing the *e probability density function of the sojourn time qi is probability density functions (PDF) of the travelling times, assumed to be known. Next, uniform probability density and then estimating the characteristic time parameters of the functions will be considered (Figure 8), but any other SP-TPN model (i.e., the IR dynamical intervals). function can be considered. *e histograms of the collected values are computed. *e parameters αi and βi correspond to the limit values of these 4.2.1. A Graphical Representation of Effective Sojourn Time histograms. *e shape of the PDF is determined from the Uncertainty. In rail transport networks, by analyzing the histogram. *ree types of PDF are considered for travelling time constraints (static intervals of the SP-TPN), which time: triangular, exponential, or uniform PDF. Figures 6 and represent the travel and parking times, it seems practical to 7 illustrate three particular segments with PDF of different provide an intermediate state between the normal and types. For parking times, only the uniform PDF has been failure behavior, by providing a tolerance interval located considered based on the knowledge of the operators. chronologically after the proper functioning interval. In the *e triangular probability density functions (PDF) is transport system, the time travel is specific to a given sit- considered as fuzzy number. Indeed, the PDF is a contin- uation. *erefore, the system is in normal operating mode, if uous variable restricted to a distribution function μ(PDF), the travel duration “T” is in the interval noted IT, Figure 9. which satisfies the following assumptions: *e mode is qualified as degraded, if the travel duration (i) μ(PDF) is piecewise continuous belongs to the interval JT (IT ≠ JT). If the travelling time exceeds the upper bound Tm, the system is considered as (ii) μ(PDF) is a convex fuzzy set c faulty. As shown in Figure 9, for each travelling and staying (iii) μ(PDF) is a normal fuzzy set times, three time values are defined: Journal of Advanced Transportation 7
Table 1: Planned and measured times. Planned Real time Real time Station Station Planned time time T(k) T(k)
Mahdia 05:25:00 05:26:48 Sousse Bab Jédid 05:40:00 05:41:22 Ezzahra 05:29:00 05:30:17 Sousse Mohamed V 05:42:00 05:43:43 Borj Arif 05:32:00 05:34:25 Sousse Sud 05:45:00 05:48:28
Sidi Massaoud Sousse Zone 05:35:00 05:36:24 05:48:00 05:52:34 (faculty) Industrielle
Mahdia Z.T. 05:38:00 05:39:45 Sahline Ville 05:51:00 05:55:33 Baghdadi 05:42:00 05:44:19 Sahline Sabkha 05:54:00 05:57:33 Békalta 05:48:00 05:51:21 Les Hôtels 05:58:00 06:01:01 Téboulba 05:53:00 05:55:41 Aéroport 06:00:00 06:02:01 Téboulba Z.I. 05:55:00 05:58:40 La Faculté 06:06:00 06:08:00 Moknine 05:58:00 06:01:58 Monastir 06:10:00 06:21:25 Moknine Gribaa 06:01:00 06:04:15 La Faculté 2 06:24:00 06:24:24
Monastir Zone Ksar Hellal 06:03:00 06:05:15 06:26:00 06:28:24 Industrielle
Ksar Hellal Z.I. 06:05:00 06:07:28 Frina 06:28:00 06:30:05 Sayada 06:07:00 06:09:27 Khnis Bembla 06:30:00 06:33:24 Lamta 06:09:00 06:11:36 Ksibet Bennane 06:34:00 06:37:23 Bouhjar 06:11:00 06:13:49 Bouhjar 06:37:00 06:40:23 Ksibet Bennane 06:14:00 06:17:22 Lamta 06:39:00 06:43:22 Khnis Bembla 06:18:00 06:21:55 Sayada 06:41:00 06:44:43 Frina 06:20:00 06:23:05 Ksar Hellal Z.I. 06:43:00 06:47:03
Monastir Zone 06:22:00 06:27:00 HellalKsar 06:45:00 06:48:03 Industrielle
La Faculté 2 06:24:00 06:31:00 Moknine Gribaa 06:47:00 06:50:02 Monastir 06:30:00 06:37:54 Moknine 06:50:00 06:52:03 La Faculté 06:39:00 06:40:54 Téboulba Z.I. 06:53:00 06:56:20 Aéroport 06:45:00 06:46:53 Téboulba 06:56:00 06:59:21 Les Hôtels 06:47:00 06:47:54 Békalta 07:00:00 07:06:02 Sahline Sabkha 06:50:00 06:50:53 Baghdadi 07:10:00 07:13:04 Sahline Ville 06:54:00 06:52:53 Mahdia Z.T. 07:15:00 07:18:03 Sousse Zone Industrielle 06:57:00 06:57:09 Sidi Massaoud 07:18:00 07:20:34 Sousse Sud 06:59:00 07:01:39 Borj Arif 07:21:00 07:22:33 Sousse Mohamed V 07:03:00 07:05:31 Ezzahra 07:24:00 07:26:54 Sousse Bab Jédid 07:05:00 07:06:31 Mahdia 07:30:00 07:28:54
m (i) Tmin: the minimum time necessary for the travelling *erefore, we can distinguish three types of intervals: a m m time normal operating interval denoted IT � [Tmin,Tmax], a de- m m m m graded interval J � [0 ,T ⋃ [T ,T ]], and a faulty (ii) T : the maximum time tolerated for the travelling T min max c max interval [Tm, + ∞] (Figure 9). time c In order to quantify the set of possible duration qi, a m (iii) Tc : critical time not to exceed (failure occurrence) graphical representation is proposed (Figure 10). *e 8 Journal of Advanced Transportation
Station A Station B
Station A Token representing the metro Station B
Path between two stations
Figure 4: Model of a single directional segment.
P186
P78
P76
T75 T76 T77 T78
P75 P77
IS77 = [60, 120] IS75 = [60, 120]
P185
Figure 5: Catch-up places P185 and P186. possibility that a time constraint is satisfied belongs to the means implemented (manual or automatic operations, steps, interval [0, 1]. Consequently, the verification of time con- functions, and mechanisms) intended to observe the state of straints can be considered as fuzzy numbers represented by an entity (online and in real time) in order to deal with the fuzzy membership functions (Figure 10). vagaries of the system during the operating phase. *e role of *ese results (Figure 10) make it possible to highlight a monitoring system is to know the state of the process, to zones of certainty for travelling durations; a high value of provide validated data to the control system, and to improve effective sojourn time (qi ∈ IT) can guarantee a normal be- the availability and safety of the process. havior of the transport monitored system, and there are no Two types of monitoring can be distinguished: operating m traffic disturbances. Instead, a low value (qi ∈ JT ∪ ] Tc , + ∞ system and control monitoring. *e operating system implies the possibility of detecting behavioral deviation. monitoring can be broken down into two types: curative and Based on the fuzzy model (Figure 10), all system scenarios predictive monitoring (Figure 11). *e monitoring of the are developed. *e scenarios consider all possible deviations. operating system is responsible for monitoring process *en, from the fuzzy model, it is possible to deduce a set of failures which are classified into two categories: cataleptic scenarios (events sequences) bringing the system to erro- failures (sudden and complete) failures and progressive neous situations. failures (Figure 11).
5. Monitoring of the Sahel Railway Network 5.2. Monitoring Principle. In the studied transport system, the monitoring is based on the control object technique. *e 5.1. Introduction. In railway transport system, traffic dis- control objects can be connected to the places of SP-TPN turbances will occur if the degradation level exceeds the model of the Sahel railway network and can, respectively, be permissible value. *erefore, monitoring represents all the applied to perform checking and validation of the Journal of Advanced Transportation 9
Table 2: Main characteristic of the places.
Number of transition αi βi qei Shape of the histogram 14852 50 2 149 365 212 Uniform 32832 30 4 149 314 207 Triangular 52832 30 6 89 180 121 Exponential 72832 30 8 89 225 150 Uniform 92832 30 10 130 567 213 Triangular 12 48 52 50 13 347 522 408 Uniform 15 38 42 40 16 208 386 268 Uniform 17 28 32 30 18 89 210 149 Triangular 19 28 32 30 20 148 269 194 Triangular 21 28 32 30 22 30 115 97 Uniform 23 28 32 30 24 29 114 52 Exponential 25 28 32 30 26 29 117 80 Uniform 27 28 32 30 28 150 297 225 Uniform 29 28 32 30 30 29 108 56 Exponential 31 28 32 30 32 85 150 101 Uniform 33 28 32 30 34 126 491 188 Uniform 35 28 32 30 36 199 267 214 Exponential 37 38 42 40 38 40 153 98 Uniform 39 28 32 30 40 269 357 288 Uniform 41 28 32 30 42 141 270 201 Triangular 43 28 32 30 44 283 568 352 Uniform 45 58 62 60 46 138 232 150 Exponential 47 38 42 40 10 Journal of Advanced Transportation
Table 2: Continued.
Number of transition αi βi qei Shape of the histogram 48 150 449 355 Uniform 49 28 32 30 50 29 344 74 Exponential 51 28 32 30 52 79 213 146 Triangular 53 38 42 40 54 30 140 91 Triangular 55 28 32 30 56 148 238 184 Uniform 57 28 32 30 58 167 386 247 Uniform 59 28 32 30 60 150 312 216 Uniform 61 28 32 30 62 9 131 44 Uniform 63 48 52 50 64 89 242 119 Uniform 65 28 32 30 66 149 285 217 Triangular 67 28 32 30 68 149 280 222 Triangular 69 28 32 30 70 148 227 175 Uniform 71 28 32 30 72 19 103 79 Triangular 73 38 42 40 74 89 178 132 Exponential 75 28 32 30 76 29 118 74 Uniform 77 28 32 30 78 319 406 344 Uniform 79 38 42 40 80 471 889 668 Uniform 81 58 62 60 82 148 229 166 Exponential 83 28 32 30 84 149 362 238 Uniform 85 28 32 30 86 40 211 115 Triangular 87 28 32 30 88 199 421 286 Triangular 89 38 42 40 90 148 245 172 Exponential 91 28 32 30 92 112 285 173 Triangular 93 28 32 30 94 67 258 128 Uniform 95 28 32 30 96 29 118 62 Uniform 97 28 32 30 Journal of Advanced Transportation 11
Table 3: Parking and travelling times between Mahdia and Sidi Massaoud stations. Station Planned time Real time T(k) D(k) Parking times Travel times Mahdia 05 : 25 : 00 05 : 26 : 48 — 00 : 00 : 50 — Ezzahra 05 : 29 : 00 05 : 30 :17 00 : 03 : 29 00 : 00 : 30 00 : 02 : 59 Borj Arif 05 : 32 : 00 05 : 34 : 25 00 : 04 : 08 00 : 00 : 30 00 : 03 : 38 Sidi Massaoud 05 : 35 : 00 05 : 36 : 24 00 : 01 : 59 00 : 00 : 30 00 : 01 : 29
Histogram delay of path 9 3
2.5
2
1.5
1
Number of measurements of Number 0.5
0 450 500 550 600 650 700 750 800 850 900 Travelling times (S) Figure 6: Uniform PDF of the travelling time between the Faculty to Monastir stations (Sousse to Mahdia direction).
Histogram delay of path 21 5 4.5 4 3.5 3 2.5 2 1.5
Number of measurements of Number 1 0.5 0 250 300 350 400 450 500 550 600 Travelling times (S) Figure 7: Triangular PDF of the travelling time between the Mahdia and Faculty stations (Mahdia to Sousse direction).
Probability density function of qi qi = qei + Ω
aj bj
qi αi qie ββi qi
IRj
ISj Figure 8: Static and dynamical intervals of place pi. 12 Journal of Advanced Transportation
I T m J Tm T m T max T c min
o
Clock Xm
Normal mode Faulty mode Degraded mode Figure 9: Travelling duration and functioning mode.
Correct traffic Degraded traffic Normal mode Degraded mode Degraded traffic µ (qi) Faulty mode
1
qi
m m m 0 Tmin Tmax Tc Figure 10: Function of possibility associated with an effective sojourn time (qi).
Monitoring
Control monitoring Operating system monitoring
Predictive monitoring Curative monitoring
Figure 11: Monitoring types. adequateness and correctness of all travelling and parking duration verification (travelling and staying times). *ese durations that are introduced in the system. durations represent interval constraints. When the interval To restrict the maximum and the minimum time pe- constraints are exceeded, there is an error. riods, allowed for a particular travelling operation, and An error is defined as a discrepancy between observed or Watch-dog control objects can be utilized for the purpose. In measured value and the true or theoretically correct value or this case, if the time restrictions are violated (travelling and condition. In our study, error means a gap between mea- staying times), the considered control system is capable to sured and computed time intervals by the scheduling task. generate an immediate reaction (similar to the alarm cases). Based on the above statements, error is sometimes re- ferred to as an incipient failure. *erefore, monitoring ac- tion is taken when the system is still in an error condition, 5.3. Constraint Violation and Monitoring Task. In the i.e., within acceptable deviation and before failure occurs. transport system, the fuzzy models associated with effective *us, this study employs uncertainty of sojourn time and sojourn time (qi) and the probability density functions probability density function of the travelling times in order (PDF) monitor the system evolutions through the time to perform early railway traffic disturbances. Journal of Advanced Transportation 13
5.4. Stochastic Fuzzy Petri Nets for Monitoring (SFPNM). Much of development works has been undertaken in certain P–TPN of the monitoring fields. Monitoring tools have been μ(qi) researched, and their application to failure prevention is well reviewed. Each input and output places of the proposed SFPNM are associated with a fuzzy description. For the input places, we describe sojourn time of a mark in places and probability Monitoring task
density functions (PDF) of the travelling times (Figure 12), PDF Fuzzy rules whereas the output variables represent the monitoring task. *ese actions can be slow, normal, or urgent. SP–TPN In SFPNM, the transitions represent rules in which antecedent propositions implicate consequent propositions, Figure 12. Each rule “Fw” is associated with a certainty Figure 12: SFPNM structure. factor, which describes the confidence level of the rule.
section presents an application of the monitoring approach 5.4.1. A Definition of SFPNM. *e stochastic fuzzy Petri net to the railway network between Mahdia and Faculty station for monitoring (SFPNM) is defined as being the n-uplet: (Figure 13).
e2
Φ1 IS1 = [60, 120]; q = 99 P1 1e
P137 P138
T122
IS5 = [60, 120] = IS3 [60, 120] q = 73 IS7 = [60, 120] = 5e q3e 88 = P7 q7e 75 P3 P5
P128 IS128 = [5100, 5160] = q128e 5110 T2 T3 T4 T5 T6 T7 T1 T121 e1 IS8 = [173, 187] IS0 = [2700, 2760] q = 183 P8 8e P2 P4 P6 = q0e 2732
IS2 = [230, 250] IS4 = [172, 188] IS6 = [174, 186] q = 239 = = P0 2e q4e 187 q6e 183
P133 P135 P136 P134
Disturbance Propagation Figure 13: Example of disturbance propagation on the railway network between Mahdia and Faculty station.
Traffic disturbance degraded mode μ(q1,6)
0.59
q1,6
= T m = T m = Tm 0 756 min 984 max 1068 max + Φ2 1115 Figure 14: Function of possibility associated with an effective sojourn time (q1,6).
*e probability density calculation permits to verify at each *e histograms of the collected values allow to built iteration that the time constraints are respected during several triangular probability density functions (PDF) which can be days. *e PDF also makes it possible to check the time con- considered as a fuzzy number (Figures 15(a) and 15(b)). *e straints linking the occurrences of the two events and enable parameters αi and βi correspond to the limit values of these detecting disruptions when these constraints are violated. histograms. Journal of Advanced Transportation 15
Histogram delay of path 21 1 5 4.5 4 0.8 3.5 3 0.6 2.5
2 0.4 1.5
Number of measurements of Number 1 0.2 0.5 0 250 300 350 400 450 500 550 600 0 Travelling times 0 0.05 0.1 0.15 0.2 0.25 PDF (a) (b)
Figure 15: (a) Triangular PDF of the travelling time between Mahdia and Faculty stations (Mahdia to Sousse direction). (b) Membership function for the PDF of travelling time.
µ SFPNM PDF µ λ λ λ MT PDF1 PDF2 PDF3 Ω1.SΩ1.NΩ1.U
PDFF0 Fw MT
t
µ q1.6 δ δ δ q 1.6–1 q 1.6–2 q 1.6–3
q 1.6
Figure 16: SFPNM of the studied railway network.
Table 4: Linguistic variables associated with the inputs. Input Membership Linguistic variable
λPDF 1 Minor PDF λPDF 2 Average λPDF 3 High
δq1.6.1 Insignificant q1.6 δq1.6.2 Marginal δq1.6.3 Critical 16 Journal of Advanced Transportation
40
35
30
Monitoring task Monitoring 25
20 100 5 4.5 105 4 3.5 110 3 115 2.5 q 2 120 1.6 1.5 PDF 1 125 0.5 0 130 Figure 17: *ree-dimensional trapezoidal membership function (MT �f(q1.6,PDF)).
various defuzzification methods were explored; Table 5: Linguistic variables associated with the outputs. the best one for this particular application: the Output Membership Linguistic variable Center of Area (COA) defuzzifier; according to
Ω1.S Slow the COA method, the weighted strengths of each MT1 Ω1.N Normal output member function are multiplied by their Ω1.U Urgent respective output membership function center points and summed; finally, this area is divided by *e mission of the proposed SFPNM associated with the the sum of the weighted member function Sahel railway network (Figure 16) is to modify the control strengths, and the result is taken as the crisp models, activate urgent procedures, and decide about the outputs selective monitoring task. *ese monitoring actions can be In practice there are two fuzzy outputs to defuzzify slow, normal, urgent, predictive, or curative. (operating system or control monitoring). Analyzing the *e full set of linguistic variables associated with each data, it is noted that the appropriate task is operating system input membership is summarized in Table 4. monitoring. Similarly, Table 5 shows linguistic variables associated with the output “monitoring action.” To demonstrate the effectiveness and accuracy of the 7. Remarks monitoring approach, an example with three fuzzy rules is outlined. Consider the following fuzzy rules: *is monitoring approach can be applied to any discrete event system integrating time constraints (urban, maritime, (i) Rule 1: if the sojourn time q1.6 ∈ [756, 984] AND the rail transport networks, manufacturing system with time PDF∈ [0.0021, 0.0034], then there is a predictive constraints, etc.). *e proposed surveillance approach would monitoring lead to more efficient inspection routines and directed an- (ii) Rule 2: if the sojourn time q1.6 ∈ [950, 1000] AND ticipatory maintenance trips. the PDF∈ [0.002, 0.0069], then there is a scheduled Certainly the approach can be applied to other networks, curative monitoring but it does not cover three aspects:
(iii) Rule 3: if the sojourn time q1.6 ∈ [350, 534] AND the (i) *e first is the progression of faults: it is not easy to PDF∈ [0.024, 1], then an urgent monitoring action define, extract, or “quantity” damage; but it may be is required worthwhile to consider the history of maintenance (iv) Each rule use the operator “AND” in the premise, on a point and other relevant facts. and since it is an AND operation, the minimum (ii) *e second aspect is the deterioration process. It is criterion is used (Mamdani inference method), and not possible to wait until the component deterio- the fuzzy outputs corresponding to these rules are rates to an unrepairable status because it may be represented in Figure 17. very unsafe when it is working in this condition. (v) Next, we perform defuzzification to convert our Hence, it would be better to repair or replace the fuzzy outputs to a single number (crisp output); components before its deterioration. Journal of Advanced Transportation 17
(iii) *e third aspect is the maintenance resources Other perspective of this work is to develop maintenance (personal, tools, drawings, spare parts, etc.). When a scheduling. Scheduling involves the allocation of resources failure occurs and if drawing, maintenance teams, to tasks over time subject to temporal and capacity con- and tools are ready, the repair work can be started. straints. *e notion of maintenance scheduling in railway transport networks refers to the assignment of resources to a 8. Conclusion task in one or several connected discrete time intervals and a decision-making process with the objective of optimizing In this paper, we have proposed a stochastic fuzzy Petri net for one or more targets. In this context, it is interesting to monitoring. *e new supervision approach is based on the develop a static insertion policy. *is procedure allows us to study of effective sojourn time of the token in places and the insert the projected maintenance jobs in periods of machine evaluation of the probability density functions (PDF) of the availability, without changing the initial scheduling solution travelling times. Abnormal behaviors and traffic disturbances jobs. *is method of integration can also integrate un- are recognized with the cooperation of the sojourn time and foreseen and urgent recovery job. PDF and not due to a simple detection based on isolated sites. Our study makes the assumption that the supervised Data Availability system is modeled by stochastic timed Petri nets. *e proposed SFPNM is able to integrate uncertainty on sojourn *e data used to support the findings of this study are in- time and probability density functions (PDF) of the trav- cluded within the article. elling times related to a base of fuzzy logic rules. *e paper proposes an application of the developed Conflicts of Interest monitoring approach to the realistic railway network. *e proposed monitoring model has a double interface, one with *e authors declare that they have no conflicts of interest. the modeling model system and the second one with the behavioral model. References Simulation results of the case study of a part of the Tunisian railway network show that monitoring approach is [1] A. Hamad and K. 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